Singular values of some modular functions

We study the properties of special values of the modular functions obtained from Weierstrass P-function at imaginary quadratic points.Comment: 19 pages,corrected typo

Point counting on reductions of CM elliptic curves

We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM $\mathbf{Q}$-curves in certain cases. This generalizes earlier results of Gross, Stark, and others.Comment: Minor corrections. To appear in Journal of Number Theor

Computing Hilbert Class Polynomials

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times

Paper Session III-B - Life Support Research & Development for the Department of Energy Space Exploration Initiative

Long-term, manned space missions of the future will require an approach to life support systems in which most of the waste materials must be processed and recycled and/or local resources are utilized. The requirement for a reliable life support system has been recognized as an important component of the Space Exploration Initiative, and the Department of Energy (DOE), in conjunction with the National Aeronautics and Space Agency, is organizing a program in support of the development of this type of technology. It is quite likely that bioprocesses will be important components of the integrated system, and this will be the primary area of research and development (R&D) within the DOE national laboratories. Microbial, enzymatic, and thermochemical processing of wastes will be investigated in the initial research studies. Other research areas of interest include water and air purification by plants, microbial detection systems, biophotochemical CO2 recycle, tissue cultures for food, single-cell protein, bioadsorbents for pollutant removal, and several others. The resulting innovative technology developed for space exploration could also serve as the basis for new approaches for the processing and recycle of waste materials on Earth

Beta-decay of nuclei around Se-90. Search for signatures of a N=56 sub-shell closure relevant the r-process

Nuclear structure plays a significant role on the rapid neutron capture process (r-process) since shapes evolve with the emergence of shells and sub-shells. There was some indication in neighboring nuclei that we might find examples of a new N=56 sub-shell, which may give rise to a doubly magic Se-90 nucleus. Beta-decay half lives of nuclei around Se-90 have been measured to determine if this nucleus has in fact a doubly-magic character. The fragmentation of Xe-136 beam at the National Superconducting Cyclotron Laboratory at Michigan State University was used to create a cocktail of nuclei in the A=90 region. We have measured the half lives of twenty-two nuclei near the r-process path in the A=90 region. The half lives of As-88 and Se-90 have been measured for the first time. The values were compared with theoretical predictions in the search for nuclear-deformation signatures of a N=56 sub-shell, and its possible role in the emergence of a potential doubly-magic Se-90. The impact of such hypothesis on the synthesis of heavy nuclei, particularly in the production of Sr, Y and Zr elements was investigated with a weak r-process network. The new half lives agree with results obtained from a standard global QRPA model used in r-process calculations, indicating that Se-90 has a quadrupole shape incompatible with a closed N=56 sub-shell in this region. The impact of the measured Se-90 half-life in comparison with a former theoretical predication associated with a spherical half-life on the weak-r-process is shown to be strong

Beta-decay half-lives and beta-delayed neutron emission probabilities of nuclei in the region below A=110, relevant for the r-process

Measurements of the beta-decay properties of r-process nuclei below A=110 have been completed at the National Superconducting Cyclotron Laboratory, at Michigan State University. Beta-decay half-lives for Y-105, Zr-106,107 and Mo-111, along with beta-delayed neutron emission probabilities of Y-104, Mo-109,110 and upper limits for Y-105, Zr-103,104,105,106,107 and Mo-108,111 have been measured for the first time. Studies on the basis of the quasi-random phase approximation are used to analyze the ground-state deformation of these nuclei.Comment: 21 pages, 10 figures, article accepted for publication in Physical Review

Determination of optimal drug dose and light dose index to achieve minimally invasive focal ablation of localised prostate cancer using WST11-vascular-targeted photodynamic (VTP) therapy

Objective: To determine the optimal drug and light dose for prostate ablation using WST11 (TOOKAD® Soluble) for vascular-targeted photodynamic (VTP) therapy in men with low-risk prostate cancer. Patients and Methods: In all, 42 men with low-risk prostate cancer were enrolled in the study but two who underwent anaesthesia for the procedure did not receive the drug or light dose. Thus, 40 men received a single dose of 2, 4 or 6 mg/kg WST11 activated by 200 J/cm light at 753 nm. WST11 was given as a 10-min intravenous infusion. The light dose was delivered using cylindrical diffusing fibres within hollow plastic needles positioned in the prostate using transrectal ultrasonography (TRUS) guidance and a brachytherapy template. Magnetic resonance imaging (MRI) was used to assess treatment effect at 7 days, with assessment of urinary function (International Prostate Symptom Score [IPSS]), sexual function (International Index of Erectile Function [IIEF]) and adverse events at 7 days, 1, 3 and 6 months after VTP. TRUS-guided biopsies were taken at 6 months. Results: In all, 39 of the 40 treated men completed the follow-up. The Day-7 MRI showed maximal treatment effect (95% of the planned treatment volume) in men who had a WST11 dose of 4 mg/kg, light dose of 200 J/cm and light density index (LDI) of >1. In the 12 men treated with these parameters, the negative biopsy rate was 10/12 (83%) at 6 months, compared with 10/26 (45%) for the men who had either a different drug dose (10 men) or an LDI of <1 (16). Transient urinary symptoms were seen in most of the men, with no significant difference in IPSS score between baseline and 6 months after VTP. IIEF scores were not significantly different between baseline and 6 months after VTP. Conclusion: Treatment with 4 mg/kg TOOKAD Soluble activated by 753 nm light at a dose of 200 J/cm and an LDI of >1 resulted in treatment effect in 95% of the planned treatment volume and a negative biopsy rate at 6 months of 10/12 men (83%)

Evidence and theory for lower rates of depression in larger US urban areas

It is commonly assumed that cities are detrimental to mental health. However, the evidence remains inconsistent and at most, makes the case for differences between rural and urban environments as a whole. Here, we propose a model of depression driven by an individual’s accumulated experience mediated by social networks. The connection between observed systematic variations in socioeconomic networks and built environments with city size provides a link between urbanization and mental health. Surprisingly, this model predicts lower depression rates in larger cities. We confirm this prediction for US cities using four independent datasets. These results are consistent with other behaviors associated with denser socioeconomic networks and suggest that larger cities provide a buffer against depression. This approach introduces a systematic framework for conceptualizing and modeling mental health in complex physical and social networks, producing testable predictions for environmental and social determinants of mental health also applicable to other psychopathologies